Adverse Selection, Reputation and Sudden Collapses in Securitized Loan Markets
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1 Adverse Selection, Reputation and Sudden Collapses in Securitized Loan Markets V.V. Chari, Ali Shourideh, and Ariel Zetlin-Jones University of Minnesota & Federal Reserve Bank of Minneapolis November 29, 2010
2 Collapses in Securitized Markets New issuances of asset-backed securities seem to collapse abruptly Collapses associated with fall in collateral values of underlying loans Policymakers perceive collapses as associated with increased inefficiency Policymakers propose policies intended to remedy increased inefficiency
3 What We Do Develop model with abrupt collapses in securitized loan markets Collapses in model associated with increased inefficiency Collapses in model associated with fall in collateral values Use model to evaluate actual and proposed policies
4 Illustration of Abrupt Collapses New Issuances of ABSs in 2000s $Bln Other Non-U.S. Residential Mortgages* Student Loans Credit Cards Autos Commercial Real Estate Subprime Home Equity $Bln *No reliable data for Non-US RMBS after Q3 '08 Source: Morganmarkets, JP Morgan Chase 0 Market collapsed in Aug 2007, Land prices fall in 2007
5 Illustration of Abrupt Collapses Change in Stock of Real Estate Bonds in 1920s $Bln Note: Data is annual change in real estate bonds divided by Nominal GDP at relevant year multiplied by Nominal GDP Source: Carter, et. al., Historical Statistics, (2006)Series Dc $Bln Market collapsed in Aug 1929
6 Perception of Increased Inefficiency Treasury Department on Public-Private Partnership, 2009: Secondary markets have become highly illiquid, and are trading at prices below where they would be in normally functioning markets. NY FED on TALF, 2009: Nontraditional investors such as hedge funds, which may otherwise be willing to invest in these securities, have been unable to obtain funding from banks and dealers because of a general reluctance to lend.
7 Our Contribution Analyze role of reputation in adverse selection models Show reputation and adverse selection lead to inefficiency and fragility Fragility: Multiple Equilibria Small aggregate shock to collateral values causes big aggregate fluctuations
8 Fragility Fall in collateral value exacerbates adverse selection problem Induces fluctuations in volume for bank with particular reputation Dynamics induce clustering of reputations Fall in collateral value can induce large fluctuations in volume
9 Policy Analysis Toxic asset purchases do not work e.g., Public-Private Partnership Program, TALF Big transfer to banks At best, leaves allocations unchanged Decrease in financing cost does not work e.g., increased FDIC guarantees Exacerbates the adverse selection problem At best, leaves allocations unchanged
10 Related Literature Adverse Selection in asset markets: Garleanu-Pedersen, Duffie-DeMarzo Reputation literature: Milgrom-Roberts, Kreps-Wilson, Mailath-Samuelson, Ordonez Global Games: Carlson-Van Damme, Morris-Shin Noisy private signals can resolve coordination problems Fragility Policy Analysis: Phillipon and Skreta 2009
11 Related Literature: Evidence of Asymmetric Information Loan originators/bank: more information than loan purchasers Downing, Jaffee, and Wallace 2009: Higher ex-post return for unsecuritized loans Drucker and Mayer 2008: Underwriters behavior in secondary market: Bid on good ex-post tranches Avoid bidding on bad ex-post tranches
12 Related Literature: Evidence of Asymmetric Information Elul 2009: Returns on securitized and held loans similar before 2006 Returns on securitized loans lower after 2006 Ivashina 2009: Evidence of information asymmetry in syndicated loans Benmelech, et. al 2010: No difference in CLOs Sufi and Mian 2009: Securitized loans more likely to default than non-securitized loans
13 Outline Securitized Loan Market Model Characterize Equilibria with Private Information: Multiplicity Perturbation: Uniqueness and Fragility Policy Analysis
14 Securitized Loan Market Model
15 Environment 2 period model - extended in paper to any horizon 1 Bank and competitive buyers All are risk neutral Bank s discount factor: β Buyers live for one period
16 Bank s Quality Type Bank quality type, indexed by loan quality: π Two quality types: π {π, π}, π < π Quality type persistent: same for both periods Bank of type π originates a loan with returns: v = v with Prob. π v = v with Prob. 1 π Initial prior on Bank s type: µ 1 = Pr(π = π)
17 Bank s Cost Type Bank s cost of holding loan relative to the market-place: c {c, c}, c < 0 < c c i.i.d. across periods Pr(c = c) = α Cost represents specialization benefits: Servicing costs Default renegotiation costs Risk tolerance or covariance of loan with bank s portfolio Funding liquidity shocks
18 Bank Bank indexed by quality type and cost type: (π,c) Bank types are private information After origination, bank chooses to sell or hold loan
19 Markets Securitized Loan Market: Buyers offer price for any assets for sale: p Buyers make simultaneous offers
20 Timing red: private information t=1 Bank s realized Bank s c realized Bank originates loan
21 Timing red: private information t=1 Buyers offer p in sec. Bank s realized Bank s c realized Bank originates loan
22 Timing red: private information t=1 Buyers offer p in sec. Bank sells Bank s realized Bank s c realized Bank originates loan Bank holds
23 Timing red: private information t=1 Buyers offer p in sec. Bank sells v realized Bank s realized Bank s c realized Bank originates loan Bank holds v realized
24 Timing red: private information t=2 v realized v=v t=1 Buyers offerp in sec. Bank sells v=v Bank s realized Bank sc realized Bank originates loan Bank holds v realized
25 Bank Payoffs Bank type: (π, c) Period Payoffs (Normalize v = 0 for now) Sell: p Hold: π v c
26 Buyer Payoffs Buyer payoffs: E π,c [v (π,c) sells] p
27 Equilibrium We consider Perfect Bayesian Equilibrium of this game Bertrand competition among buyers in each period
28 Full Information Benchmark Bank sells if and only if p π v c For known quality type, break even prices are p = π v At break even prices: π v π v c sell if and only if c 0
29 Full Information Benchmark Hold/Sell decision depends only on costs not on π (, c) Bank has comparative advantage: hold (, c) Market has comparative advantage: sell Efficiency: allocate loans to agents with comparative advantage
30 Characterizing Equilibria with Private Information
31 Equilibria with Private Information We will show: Uniqueness in the static game/last period Multiplicity in dynamic game Multiplicity only because of reputation
32 Simplification Can show in any equilibrium, in each period and after every history (, c) : hold loans (π, c) sells loans Focus on high quality, high cost bank ( π, c) For presentation, fix decisions of remaining banks: (, c) hold (π, c) sell
33 Characterizing Equilibria with Private Information Last Period/Static Game
34 Characterizing Equilibria Unique equilibrium which depends on parameter µ 2 µ 2 : reputation in dynamic model If µ 2 is low: Lemons problem - Price is low - ( π, c) bank holds loan If µ 2 is high: No lemons problem - Price is high - ( π, c) bank sells loan
35 Break Even Prices Two candidate equilibrium prices: ( π, c) bank sells: p sell (µ 2 ) = (µ 2 π + (1 µ 2 )π) v ( π, c) bank holds: p hold = π v
36 Static Equilibrium Characterization Selling is an equilibrium if and only if p sell (µ 2 ) π v c There exists µ such that ( π, c) bank is indifferent If µ 2 µ, Selling is optimal; Bertrand Competition If µ 2 < µ, Holding is optimal µ critical threshold, above which ( π, c) bank sells in equilibrium
37 How Equilibrium Depends on Reputation Last period equilibrium depends only on reputation, µ 2 Hold Sell 0 1 Defines a value function V 2 (µ 2 ): increasing and convex.
38 Summarizing Equilibrium Bank s last period ex-ante cost Value Function V 2 (µ 2 ) π v E[c] µ µ 2 0 1
39 Efficiency of Equilibrium in a Static Model Can show equilibrium is interim efficient Argument similar to Myerson (1983) Obvious point: Adverse Selection does not necessarily imply inefficiency
40 Characterizing Equilibria with Private Information First Period
41 Characterizing Equilibria Focus on period 1 strategies and learning rule Unique equilibrium for extreme reputations Multiple equilibria for intermediate reputations
42 Characterizing Equilibria Multiple equilibria for intermediate reputations:
43 Characterizing Equilibria Multiple equilibria for intermediate reputations: Positive Reputational Equilibrium: - First period price is high - ( π, c) bank sells loan in the 1st period
44 Characterizing Equilibria Multiple equilibria for intermediate reputations: Positive Reputational Equilibrium: - First period price is high - ( π, c) bank sells loan in the 1st period Negative Reputational Equilibrium: - First period price is low - ( π, c) bank holds loan in the 1st period
45 Multiple Equilibria Positive Reputational Equilibrium Sell 0 1 Hold Negative Reputational Equilibrium
46 Recall Timing t=2 v realized v=v t=1 Buyers offerp in sec. Bank sells v=v Bank s realized Bank sc realized Bank originates loan Bank holds v realized
47 Bank s Best Response Value of Sell: p + β( πv 2 (µ s v ) + (1 π)v 2 (µ s0 )) Value of Hold: π v c + βv 2 (µ h ) Selling optimal if and only if: p sell (µ 1 ) + β [ πv 2 (µ s v ) + (1 π)v 2 (µ s0 ) V 2 (µ h )] π v c }{{} reputational gain
48 Bank s Best Response Value of Sell: p + β( πv 2 (µ s v ) + (1 π)v 2 (µ s0 )) Value of Hold: π v c + βv 2 (µ h ) Selling optimal if and only if: p sell (µ 1 ) + β [ πv 2 (µ s v ) + (1 π)v 2 (µ s0 ) V 2 (µ h )] π v c }{{} reputational gain µ s v,µ s0,µ h different in two equilibria
49 Updating by Future Buyers Positive Beliefs: ( π, c) sells (π, c) sells (,c) holds Signal used to update 1 µ 2 µ H µ S v µ S0 0 0 µ 1 1
50 Updating by Future Buyers Positive Beliefs: ( π, c) sells (π, c) sells (,c) holds Signal used to update Negative Beliefs: ( π, c) holds (π, c) sells (,c) holds Signal ignored in updating 1 µ 2 1 µ 2 µ H µ S v µ H µ S0 0 0 µ 1 1 µ S v = µ S0 = µ 1 1
51 Bank s Best Response, Positive Beliefs Positive beliefs: selling allows future buyers to see asset quality ( π, c) bank has bigger incentive to sell than in static model For µ 1 < µ (Static Cutoff), πv 2 (µ s v ) + (1 π)v 2 (µ s0 ) V 2 (µ h ) > 0 by convexity of V 2 and learning (Eµ µ 1 = µ h ) ( π, c) banks with reputation below static threshold also sell
52 Positive Reputational Equilibrium Proposition There exists an equilibrium in which ( π, c) bank chooses sell for µ 1 [µ,1], µ < µ Sell 0 1
53 Bank s Best Response, Negative Beliefs Negative beliefs: selling signals low quality type, independent of realized return ( π, c) bank has bigger incentive to hold than in static model For µ 1 > µ, πv 2 (µ s v ) + (1 π)v 2 (µ s0 ) V 2 (µ h ) < 0 ( π, c) banks with reputation above static threshold also hold
54 Negative Reputational Equilibrium Proposition There exists an equilibrium in which ( π, c) bank chooses hold for µ 1 [0, µ] µ > µ 0 1 Hold
55 Multiplicity Positive Reputational Equilibrium Sell 0 1 Hold Negative Reputational Equilibrium For µ 1 [µ, µ], Multiplicity of equilibria
56 Efficiency Interim Dominance Under sufficient conditions, positive outcome interim dominates negative Ex-ante Dominance Under sufficient conditions, positive outcome ex-ante dominates negative
57 Multiplicity Multiplicity can be interpreted as fragility Suppose sunspot induces shift to negative equilibrium Can induce sudden collapse Sunspot can be fall in collateral values
58 Multiplicity Cannot do policy analysis with multiple equilibria Need refinement Our perturbation: Shocks to default values of collateral Unique and fragile equilibrium
59 Adding Aggregate Shocks
60 Aggregate Shocks Default value v F(v) In static model, ( π, c) sells if [µ π + (1 µ)π] v+[µ(1 π) + (1 µ)(1 π)] v π v+(1 π)v c or, setting v = v v [µ π + (1 µ)π] v π v c Fall in v implies v increases Raises µ 2
61 Aggregate Shocks and Fragility In static model, can get fragility if many banks reputations are clustered No reason to expect this Perturbation yields unique equilibrium Dynamic model yields clustering
62 Aggregate Shocks and Perturbation v a random variable, v F(v) Banks and buyers in period 1 observe signal of v: v 1 = v + σɛ, Eɛ = 0, E[v v 1 ] = v 1 Period 2 buyers do not observe v 1 or prices in period 1 Bank and period 2 buyers observe v
63 Perturbation t=1 Bank sells/holds t=2 Buyers update belief Bank sells/holds Buyers offer p 1 Buyers offer p 2
64 Perturbation t=1 Banks and period 1 buyers learn v 1 = v + Bank sells/holds t=2 Buyers update belief Bank sells/holds Buyers offer p 1 Buyers offer p 2 Bank and Period 2 buyers learn v
65 Uniqueness of Equilibrium Theorem As σ 0, the set of equilibrium strategies for the ( π, c) bank converges to a unique strategy given by Sell if v 1 v 1, Hold if v 1 < v 1.
66 Cutoff Thresholds v 6 5 v (µ) SELL HOLD µ
67 Idea of Proof Reputational incentives depend on future buyer s belief about ( π, c) bank s action in 1st period Reputational incentives are bounded Dominance regions: Very high v 1 : ( π, c) bank sells independent of future beliefs Very low v 1 : ( π, c) bank holds independent of future beliefs
68 Idea of Proof Limit dominance restrictions on learning Restricted learning: tighter bounds on reputational incentives Iterating in this manner: Convergence
69 Invariant Distribution of Reputation µ Invariant distribution of reputations of π banks (with exogenous replacement)
70 Volume of Trade v
71 Sudden Collapses Have shown sudden adverse selection plus learning means sudden collapses can affect many banks Shocks to collateral values can lead to big effects on aggregate new issues
72 Policy Analysis
73 Policy Analysis Policies that Do Not Work
74 Loan Purchase Policies Public-Private Partnership for Legacy Assets TALF
75 Loan Purchase Policies Consider the selected unique equilibrium of two period game: Recall: low collateral value: hold, high collateral value: sell Contingent on a low collateral value, government offers to buy loans Government uses prices associated with positive reputational equilibrium
76 Loan Purchase Policies Equivalent to an offer by buyer Gov t policy has no effect on reputational gain Negative reputational outcomes still equilibrium Loan purchase policy induces no change in bank behavior Loan purchase policy results in transfer to (π, c) banks
77 Policies Subsidizing Debt Finance Government reduces interest rates in period 1 Greater incentives to hold rather than sell Worsens lemons problem Negative reputational outcomes still equilibrium
78 Policies Subsidizing Debt Finance Government reduces interest rates in period 1 Greater incentives to hold rather than sell Worsens lemons problem Negative reputational outcomes still equilibrium Real world policies: Increase in FDIC guarantees
79 Policies Subsidizing Debt Finance Government reduces interest rates in period 2 Unperturbed game: smaller region for multiplicity in period 1 Perturbed game: Ambiguous Interest rate policy: time inconsistent
80 Policy Analysis Policies that Might Work
81 Forced Loan Sales Government forces banks to sell random fraction of loans No lemons problem Loses comparative advantage benefit
82 Commitment to Future Purchases Policy Suppose government can commit to making future purchases contingent on signals. Solves multiplicity problem Why can t private agents commit?
83 Future Work Endogenize loan origination What effect does secondary market collapse have on origination? Uniquely implement the efficient equilibrium
84 Conclusions Develop model with sudden collapses Sudden collapses associated with increased inefficiency Sudden collapses likely when collateral values fall Proposed and implemented policies do not work Other policies might be better
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